The purpose of this paper is to extend the existing axiom scheme for quantum field theory to include most known examples of gauge theories. The axioms are formulated to be neutral relative to possible implementation strategies. They are developed in both the Euclidean and Minkowski metrics for spacetime. We demonstrate that the Euclidean axioms imply the Minkowski (Wightman) axioms. The reconstruction theorem for gauge fields as operator-valued tempered distributions with gauge transformation properties is proven as well.